Solving the Physics Behind a Reddit Comic: Can the Raptor Catch Up?

[winowmak3r]

Homework Statement

I like to visit reddit. Browsing I found this comic:

I'm assuming sea level.

Speed of sound: 340.29m/s

Homework Equations

Wavelength = velocity of wave / frequency

change in frequency = -(velocity source - velocity reciever) / wavelength
(SOURCE: http://en.wikipedia.org/wiki/Doppler_effect)

The Attempt at a Solution

My general method of solving this problem would be to find the wavelength of the raptor's war cry, then once I know that I can figure out how fast the raptor is traveling using the change in frequency formula.

I'm assuming the raptor's war cry is traveling at the speed of sound at sea level:

wavelength = (340.29m/s) / 1260Hz = .27007 m/cycle

Solving for the velocity of the source in the change in frequency equation I get:

-(change in frequency)*(wavelength)+(velocity of receiver) = (velocity of source)
-(60Hz)*.27007m/cycle+9m/s = 7.2m/s

The raptor has a lower velocity than the person, so the raptor will never catch up with him. However, a velocity of a human of 9m/s is Olympic sprinter speed, so am I correct to assume the person will still get eaten because a human can't keep that constant running velocity?

I realize the comic is probably just someone making stuff up without doing the math, so I'm wondering if my solution is correct. I'm pretty sure the math is sound, but without any confidence that the problem is realistic (like the problems I usually encounter) I have no idea if my solution is reasonable.

By the way, this is purely for entertainment purposes. I just enjoy solving stuff like this, it's a nice break from the really hard (and sometimes boring) stuff.

 

[davo789]

I don't *think* that can be quite right. The fact that the frequency received is higher than the emitted frequency suggests that the velociraptor is moving towards the person. I'll have a look at the equations a bit later!

 

[winowmak3r]

My thoughts exactly. However, I think the problem is that the difference in frequency observed from the emitted is simply not large enough. As the raptor moves towards the person, the frequency should get larger as the raptor increases in velocity, correct? As I've said before, I just don't think the numbers for the frequency observed is correct for something that is supposed to be moving faster than 9m/s.

I get a -7.2m/s as my final velocity, but I took the absolute value of it because I didn't really set an initial frames of reference or anything. Could it be, perhaps, that the raptor is moving at 9m/s + 7.2m/s, that the velocity I got is really how fast the raptor is approaching the person relative to the person's velocity? So the raptor is really going something like 16.2m/s. Now I'm not so confident I've got it right. Any insight would be appreciated!

 

[davo789]

The fact that the measured frequency is higher than the emitted frequency suggests that the dinosaur is gaining on the person. Its like running away from a police car; although the increase might not be as large, the frequency is still higher and the police car is definitely catching you up!